Americans purchase nearly 3 billion batteries (dry-cells) every year. On average, each person in the US disposes of 8 batteries every year (PKIDs, 2009). A rechargeable battery can replace hundreds of single-use batteries over its life. Also, all batteries contain metals such as mercury, lead, cadmium, nickel and lithium, which may contaminate the environment if disposed of improperly, hence reducing consumption eases the strain on natural resources.
During Operation Iraqi Freedom, the Marines used an estimated average of 3,028 batteries per day, which was half the requirement of the entire battlefield. Apart from the issue of increasing efficiency, and reducing cost and wastage, rechargeable batteries are a key enabling technology for solving energy problems of the future. One key feature of renewable energy sources, such as solar, wind, tidal, hydropower, etc. is that these sources are not continually available. A report by the California ISO Board notes that, “Wind generation energy production is extremely variable, and in California, it often produces its highest energy output when the demand for power is at a low point” (CA ISO, 2008). An energy storage facility coupled with these power generation sources would make these solutions more economically feasible. Such energy storages, comprising batteries, fuel cell or super-capacitors, would in turn need reliable health monitoring systems to ensure viable levels of system availability, reliability and sustainability and to protect the assets from degradation due to non-optimal usage. Battery health management will also play a critical role in electric vehicles that will be dependant on an accurate gauge for remaining electrical charge and for trade-offs in long-term durability and short-term usage needs.
A primary purpose of modeling battery aging is to enable effective battery health monitoring (BHM) applications that ensure that the battery operation stays within design limits and to provide warning or mitigate damage when these limits are exceeded. Current BHM efforts come in many flavors, from the data-driven (Rufus et al., 2008) to the model-based (Plett, 2004) and even hybrid approaches (Goebel et al., 2008). Implementation complexity can range from intermittent manual measurements of voltage and electrolyte specific gravity to fully automated online supervision of various measured and estimated battery parameters using dynamic models. The sophistication of the models also varies from a collection of basis functions (Stamps et al., 2005) to detailed formulations derived from physical analysis of the cell (Hartley and Jannette, 2005).
Viewing the issue from the applications perspective, researchers in the aerospace domain have examined the various failure modes of the battery subsystems. Different diagnostic methods have been evaluated, like discharge to a fixed cut-off voltage, open circuit voltage, voltage under load and electrochemical impedance spectrometry (EIS) (Vutetakis and Viswanathan, 1995). In the field of telecommunications, workers have sought to combine conductance technology with other measured parameters like battery temperature/differential information and the amount of float charge (Cox and Perez-Kite, 2000).
Other workers have concentrated more on the prognostic approach than on the diagnostic one. Statistical parametric models have been built to predict time to failure (Jaworski, 1999). Electric and hybrid vehicles have been another fertile area for battery health monitoring (Meissner and Richter, 2003). Impedance spectroscopy has been used to build battery models for cranking capability prognosis (Blanke et al., 2005). State estimation techniques, such as the Extended Kalman Filter (EKF), have been applied for real-time prediction of state-of-charge (SOC) and state-of-life (SOL) of automotive batteries (Bhangu et al., 2005; Plett, 2004). A decision-level fusion of data-driven algorithms, such as Autoregressive Integrated Moving Average (ARIMA) and neural networks, has been investigated for both diagnostics and prognostics (Kozlowski, 2003). As the popular cell chemistries changed from lead acid to nickel metal hydride to lithium ion, cell characterization efforts have kept pace. Dynamic models for the lithium ion batteries that take into consideration nonlinear equilibrium potentials, rate and temperature dependencies, thermal effects and transient power response have been built (Gao et al., 2002; Hartmann II, 2008; Santhanagopalan et al., 2008).
However, a need still exists for a flexible prognostics framework that combines the sensor data from battery monitors, the models developed, and the appropriate state estimation and prediction algorithms, in the form of an integrated BHM solution.
Battery Characteristics.
Batteries are essentially energy storage devices that facilitate the conversion, or transduction, of chemical energy into electrical energy, and vice versa (Huggins, 2008). A battery includes a pair of electrodes (anode and cathode) immersed in an electrolyte and sometimes separated by a separator. The chemical driving force across the cell is due to the difference in the chemical potentials of its two electrodes, which is determined by the difference between the standard Gibbs free energies the products of the reaction and of the reactants. The theoretical open circuit voltage, E0, of a battery is measured when all reactants are at 25° C. and at 1M concentration or 1 atm pressure. However, this voltage is not available during use, due to the various passive components inside like the electrolyte, the separator, terminal leads, etc. The voltage drop due to these factors can be mainly categorized as:                IR drop—This drop in cell voltage is due to the current flowing across the internal resistance of the battery.        Activation polarization—This term refers to the various retarding factors inherent to the kinetics of an electrochemical reaction, like the work function that ions must overcome at the junction between the electrodes and the electrolyte.        Concentration polarization—This factor takes into account the resistance faced by the mass transfer (e.g. diffusion) process by which ions are transported across the electrolyte from one electrode to another.        
FIG. 1 illustrates a typical polarization curve of a battery with the contributions of all three of the above factors shown as a function of the current drawn from the cell. Since, these factors are current-dependent, i.e. they come into play only when some current is drawn from the battery, the voltage drop caused by them usually increases with increasing output current.
Because the output current plays such a big role in determining the losses inside a battery, it is an important parameter to consider when comparing battery performance. The term most often used to indicate the rate at which a battery is discharged is the C-Rate (Huggins, 2008). The discharge rate (C-rate) of a battery is expressed as C/r, where r is the number of hours required to completely discharge the nominal capacity of the battery. Thus, a 2 Amp-hour battery discharging at a rate of C/10 or 0.2 Amps would last for 10 hours. The terminal voltage of a battery, and the charge delivered, can vary appreciably with changes in the C-Rate. Further, the amount of energy supplied, related to the area under the discharge curve, is also strongly C-Rate dependent. FIG. 2 illustrates a typical discharge of a battery and its variation with C-Rate. Each curve corresponds to a different C-Rate or C/r value (the lower the r the higher the current) and assumes constant temperature conditions.
Moving on from the theoretical aspects to the application point of view, the relevant physical properties of a battery may be different in different cases. Sometimes specific energy and specific power (energy and power available per unit weight) are important, as in vehicle propulsion applications. Other times the amount of energy stored per unit volume, called the energy density, can be more important for batteries that power portable electronic devices, like cell-phones, laptop computers, cameras, etc., while power per unit volume, known as power density, can be important for some uses like cordless power tools. However, in recent times when the use of rechargeable batteries is proliferating in consumer products, an important parameter to consider is cycle life, which is the number of times a battery can be recharged before its capacity has faded beyond acceptable limits (typically about 20-30 percent).
The degradation of battery capacity with aging, as manifested by the cycle life parameter, can be modeled using Coulombic efficiency ηC, defined as the fraction of the prior charge capacity that is available during the following discharge cycle (Huggins, 2008). This depends upon a number of factors, especially current and depth of discharge in each cycle. The temperature at which batteries are stored and operated under also has a significant effect on the Coulombic efficiency. FIG. 3 illustrates the degradation of battery capacity with increase of cycles for different values of Coulombic efficiency. Note how even a small inefficiency factor of 0.5 percent (Coulombic efficiency=0.995) can reduce the capacity by about 60 percent within 100 cycles.